Longitudinal Seismic Analysis Of Tunnel Considering Dynamic Equivalent Stiffness

With the rapid development of China's economy and transportation,the underground space structure has been built on a large scale.Among them,the tunnel is one of the main forms of underground space structure,but due to the severe damage caused by the earthquake,explosion and human factors,the analysis of its seismic performance needs to be studied urgently.At present,the research on the seismic performance of tunnels is still imperfect,and it mainly focuses on the seismic research in the cross-section of tunnels,while the longitudinal seismic research is relatively less.Among various methods for seismic analysis,the response displacement method is widely used in the seismic analysis of underground structures because it can better consider the deformation of underground structures under seismic action.However,it is difficult to accurately calculate the foundation spring stiffness because the unified theoretical formula has not been established.The dynamic equivalent stiffness of elastic foundation beam can be expressed as the foundation spring stiffness and radiation damping.It can be used for seismic analysis of underground structures to obtain more accurate results.Therefore,this paper considers the dynamic equivalent stiffness of elastic foundation beam to replace the ground spring stiffness and analyzes the longitudinal seismic performance of tunnel through theoretical derivation and numerical simulation.The main contents and conclusions of the study are as follows:(1)Based on the basic equation of elastic dynamic space theory,considering the dynamic interaction between elastic foundation beam and elastic half-space,the analytical expressions of the vertical and horizontal dynamic equivalent stiffness of elastic foundation beam are obtained through theoretical derivation.The various rules of the vertical and horizontal dynamic equivalent stiffness of elastic foundation beam are discussed through parameter analysis.The results show that the vertical and horizontal dynamic equivalent stiffness of elastic foundation beam are not constant,but vary with the phase velocity of wave propagation in the beam.(2)Based on the response displacement method,the tunnel is simulated as an elastic foundation beam.By using the vertical and horizontal dynamic equivalent stiffness,the analytical expressions of maximum bending moment and axial force of tunnel in elastic phase and the analytical expression of maximum axial force in plastic phase are obtained by theoretical derivation.The force of the tunnel under seismic action is analyzed through numerical examples.The results show that when the incident angle of the seismic wave is 0°,the bending moment of tunnel is the largest,and when the incident angle is 45°,the axial force of tunnel is the largest.(3)The finite element software ABAQUS is used to simulate the force of the tunnel under seismic action.The longitudinal seismic performance of tunnel is studied,and the simulation results are compared with the theoretical analysis results.The results show that the simulated and theoretical values of tunnel bending moment and axial force are similar,which proves the correctness and reliability of the theoretical analysis.This paper enriches the research on the seismic performance of tunnel structures and provides theoretical support for the seismic design of tunnels.